Thoughts about Completing the Square and Quadratic Formula

Completing the square is so difficult for many students.  There are setup issues to deal with (like not having the x^2 coefficient as 1), finding the b/2 term squared, and maintaining the b/2 in the next line, and then the process of simplifying the results.

However, students seem to really like the quadratic formula (which is awesome) because they like that you can just plug and chug.

Today’s warmup was me reviewing a completing the square HW problem, and then the students began solving a few completing the square problems.  It did seem that a few of them got the hang of it (mostly the students with stronger procedural fluency and organization), but the students that did not get it were the ones that struggled with making the leap from using a standard-form quadratic, and figuring out a way to get it in the form (x+a)^2.

For the quadratic formula, I used a story as a mnemonic to help the students memorize the elements of it.

“A negative boy debated the pros and cons of going to a radical party.  He decided to be a square boy and missed out on four awesome chicks.  But that’s okay, because it was all over by 2am.”

They liked this, chuckled a bit, and thought it was cheesy but helpful.  We practiced one problem, and students began their homework of using the quadratic formula.

Something that I still need to work on is getting kids to raise their hand instead of shouting out.  One thing I should do is calmly reply, “Please raise your hand” and WAIT till they do so.